Localizability in de Sitter space

TL;DR

This paper constructs a Newton-Wigner-like position operator for a scalar field in de Sitter space, establishing its properties and evolution, thus advancing understanding of localization in curved spacetime.

Contribution

It introduces a de Sitter space analogue of the Newton-Wigner position operator and proves its uniqueness and well-defined evolution.

Findings

Defined a de Sitter Newton-Wigner position operator.

Proved the existence and uniqueness of the operator.

Derived a simple expression for its time evolution.

Abstract

An analogue of the Newton-Wigner position operator is defined for a massive neutral scalar field in de Sitter space. The one-particle subspace of the theory, consisting of positive-energy solutions of the Klein-Gordon equation selected by the Hadamard condition, is identified with an irreducible representation of de Sitter group. Postulates of localizability analogous to those written by Wightman for fields in Minkowski space are formulated on it, and a unique solution is shown to exist. A simple expression for the time-evolution of the operator is presented.